The explicit forms and zeros of the Bergman kernel function for Hartogs type domains

Heungju Ahn; Jong Do Park

doi:10.1016/j.jfa.2012.01.021

The explicit forms and zeros of the Bergman kernel function for Hartogs type domains

Heungju Ahn, Jong Do Park

School of Undergraduate Studies

Korea Institute for Advanced Study

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We define the Cartan-Hartogs domain, which is the Hartogs type domain constructed over the product of bounded Hermitian symmetric domains and compute the explicit form of the Bergman kernel for the Cartan-Hartogs domain using the virtual Bergman kernel. As the main contribution of this paper, we show that the main part of the explicit form of the Bergman kernel is a polynomial whose coefficients are combinations of Stirling numbers of the second kind. Using this observation, as an application, we give an algorithmic procedure to determine the condition that their Bergman kernel functions have zeros.

Original language	English
Pages (from-to)	3518-3547
Number of pages	30
Journal	Journal of Functional Analysis
Volume	262
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2012.01.021
State	Published - 15 Apr 2012

Bibliographical note

Funding Information:
✩ This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (MEST) (NRF-2010-0024633 for the first author) and (NRF-2009-0076417 for the second author). * Corresponding author. E-mail addresses: [email protected] (H. Ahn), [email protected], [email protected] (J.-D. Park).

Keywords

Bergman kernel
Bounded symmetric domain
Hartogs domain
Routh-Hurwitz theorem
Stirling number of the second kind
Virtual Bergman kernel

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10.1016/j.jfa.2012.01.021

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title = "The explicit forms and zeros of the Bergman kernel function for Hartogs type domains",

abstract = "We define the Cartan-Hartogs domain, which is the Hartogs type domain constructed over the product of bounded Hermitian symmetric domains and compute the explicit form of the Bergman kernel for the Cartan-Hartogs domain using the virtual Bergman kernel. As the main contribution of this paper, we show that the main part of the explicit form of the Bergman kernel is a polynomial whose coefficients are combinations of Stirling numbers of the second kind. Using this observation, as an application, we give an algorithmic procedure to determine the condition that their Bergman kernel functions have zeros.",

keywords = "Bergman kernel, Bounded symmetric domain, Hartogs domain, Routh-Hurwitz theorem, Stirling number of the second kind, Virtual Bergman kernel",

author = "Heungju Ahn and Park, \{Jong Do\}",

note = "Funding Information: ✩ This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (MEST) (NRF-2010-0024633 for the first author) and (NRF-2009-0076417 for the second author). * Corresponding author. E-mail addresses: [email protected] (H. Ahn), [email protected], [email protected] (J.-D. Park).",

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AU - Park, Jong Do

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N2 - We define the Cartan-Hartogs domain, which is the Hartogs type domain constructed over the product of bounded Hermitian symmetric domains and compute the explicit form of the Bergman kernel for the Cartan-Hartogs domain using the virtual Bergman kernel. As the main contribution of this paper, we show that the main part of the explicit form of the Bergman kernel is a polynomial whose coefficients are combinations of Stirling numbers of the second kind. Using this observation, as an application, we give an algorithmic procedure to determine the condition that their Bergman kernel functions have zeros.

AB - We define the Cartan-Hartogs domain, which is the Hartogs type domain constructed over the product of bounded Hermitian symmetric domains and compute the explicit form of the Bergman kernel for the Cartan-Hartogs domain using the virtual Bergman kernel. As the main contribution of this paper, we show that the main part of the explicit form of the Bergman kernel is a polynomial whose coefficients are combinations of Stirling numbers of the second kind. Using this observation, as an application, we give an algorithmic procedure to determine the condition that their Bergman kernel functions have zeros.

KW - Bergman kernel

KW - Bounded symmetric domain

KW - Hartogs domain

KW - Routh-Hurwitz theorem

KW - Stirling number of the second kind

KW - Virtual Bergman kernel

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DO - 10.1016/j.jfa.2012.01.021

M3 - Article

AN - SCOPUS:84862807958

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SP - 3518

EP - 3547

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

The explicit forms and zeros of the Bergman kernel function for Hartogs type domains

Abstract

Bibliographical note

Keywords

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